Experimental test of the Rosenzweig-Porter model for the transition from Poisson to Gaussian unitary ensemble statistics

• URL: http://arxiv.org/abs/2305.12840v3
• Date: Mon, 14 Aug 2023 02:35:30 GMT
• Title: Experimental test of the Rosenzweig-Porter model for the transition from Poisson to Gaussian unitary ensemble statistics
• Authors: Xiaodong Zhang, Weihua Zhang, Jiongning Che, and Barbara Dietz
• Abstract summary: We report on an experimental investigation of the transition of a quantum system with integrable classical dynamics to one with violated time-reversal (T) invariance and chaotic classical counterpart. High-precision experiments are performed with a flat superconducting microwave resonator with circular shape. We find good agreement with analytical predictions for the spectral properties of the Rosenzweig-Porter (RP) model.
• Score: 3.431306464236116
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We report on an experimental investigation of the transition of a quantum system with integrable classical dynamics to one with violated time-reversal (T) invariance and chaotic classical counterpart. High-precision experiments are performed with a flat superconducting microwave resonator with circular shape in which T-invariance violation and chaoticity are induced by magnetizing a ferrite disk placed at its center, which above the cutoff frequency of the first transverse-electric mode acts as a random potential. We determine a complete sequence of approx. 1000 eigenfrequencies and find good agreement with analytical predictions for the spectral properties of the Rosenzweig-Porter (RP) model, which interpolates between Poisson statistics expected for typical integrable systems and Gaussian unitary ensemble statistics predicted for chaotic systems with violated T invariance. Furthermore, we combine the RP model and the Heidelberg approach for quantum-chaotic scattering to construct a random-matrix model for the scattering (S) matrix of the corresponding open quantum system and show that it perfectly reproduces the fluctuation properties of the measured S matrix of the microwave resonator.

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